Find the x and y Intercepts f(x)=-2x(4x+5)(5x+5)

$f (x) = - 2 x (4 x + 5) (5 x + 5)$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 2 x (4 x + 5) (5 x + 5)$

Solve the equation.

Rewrite the equation as $- 2 x (4 x + 5) (5 x + 5) = 0$ .

$- 2 x (4 x + 5) (5 x + 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$4 x + 5 = 0$

$5 x + 5 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $4 x + 5$ equal to $0$ and solve for $x$ .

Set $4 x + 5$ equal to $0$ .

$4 x + 5 = 0$

Solve $4 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$4 x = - 5$

Divide each term in $4 x = - 5$ by $4$ and simplify.

Divide each term in $4 x = - 5$ by $4$ .

$\frac{4 x}{4} = \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 5}{4}$

Divide $x$ by $1$ .

$x = \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

Set $5 x + 5$ equal to $0$ and solve for $x$ .

Set $5 x + 5$ equal to $0$ .

$5 x + 5 = 0$

Solve $5 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$5 x = - 5$

Divide each term in $5 x = - 5$ by $5$ and simplify.

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

The final solution is all the values that make $- 2 x (4 x + 5) (5 x + 5) = 0$ true.

$x = 0, - \frac{5}{4}, - 1$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- \frac{5}{4}, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 2 \cdot 0 (4 (0) + 5) (5 (0) + 5)$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot (0 (4 (0) + 5) (5 (0) + 5))$

Simplify $- 2 \cdot (0 (4 (0) + 5) (5 (0) + 5))$ .

Multiply $4$ by $0$ .

$y = - 2 \cdot (0 (0 + 5) (5 (0) + 5))$

Add $0$ and $5$ .

$y = - 2 \cdot (0 \cdot 5 (5 (0) + 5))$

Multiply $0$ by $5$ .

$y = - 2 \cdot (0 (5 (0) + 5))$

Multiply $5$ by $0$ .

$y = - 2 \cdot (0 (0 + 5))$

Add $0$ and $5$ .

$y = - 2 \cdot (0 \cdot 5)$

Multiply $- 2 (0 \cdot 5)$ .

Multiply $0$ by $5$ .

$y = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(0, 0), (- \frac{5}{4}, 0), (- 1, 0)$

y-intercept(s): $(0, 0)$

Step 4

Find the x and y Intercepts f(x)=-2x(4x+5)(5x+5)

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